Mathematical Sciences: Integrable Models in Mathematics and Physics

数学科学：数学和物理中的可积模型

• 批准号: 9001794
• 负责人: Craig Tracy
• 金额: $ 12.45万
• 依托单位: University of California-Davis
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-01 至 1993-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9001794&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Integrable; Models; Mathematics

This research involves the quantum field theory of fermions on the Poincare disk and the hard hexagon model - a lattice gas model in statistical mechanics. The research on the quantum theory of fermions will involve expressing the Schwinger functions in terms of certain nonlinear deformation equations. These equations will then be analyzed both in the Euclidean limit and in the conformal field theory limit. An important aspect of this work is the extension of the existing theory to the noneuclidean setting which may lay the groundwork for extensions to Riemann surfaces of a more general type. The research on the hard hexagon model will involve derivations of differential equations for the partition function and density functions. An attempt will be made to extend these equations to the hard square lattice gas, a model that is 'not solvable' by present techniques. This research is in the general area of theoretical physics and deals with isomonodromy deformations and applications to conformal field theory, statistical mechanics, and scattering theory.

这项研究涉及费米子的量子场论 Poincare盘和硬六边形模型-格子气 统计力学模型 量子力学的研究 费米子的理论将涉及表达施温格 函数的某些非线性变形方程。 这些方程将在欧几里得极限下进行分析 和共形场论极限。 的一个重要方面 这项工作是现有理论的延伸， 非欧几里德设置可能奠定基础的扩展 更一般的黎曼曲面。 的研究 硬六边形模型将涉及微分的推导 配分函数和密度函数的方程。 一个 我们将尝试把这些方程推广到硬正方形 晶格气，一个目前“不可解”的模型 技术. 这项研究属于理论物理学的一般领域 并处理isomonodromy变形和应用， 共形场论、统计力学和散射 理论